I think you have already identified why your feet are in such a bad way. Nothing on your feet ? That's a sure way to cause damage to the skin and create problems with dryness, injury, callouses and general soreness. Are there chilblains too ? Plus the pathogens that you are walking on day in and day out are not good for your feet.
Wash your feet twice a day, using a gentle soap, dry thoroughly and then moisturise. Wear clean laundered socks and always wear a shoe, slipper or trainer and I am sure there will be a massive improvement. Alternate your foot wear so that they have the chance to dry completely if your feet sweat quite a bit.
I would also suggest that you should seek the advice from a podiatrist as they will get to see them and can screen you for any potential health issues which could also be a contributing factor to the dryness.
I'll pass on commenting on polish....just leave off if in doubt.
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